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# Combat Damage Formula

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Article by Kelly Chong

## Introduction

For Arithmancy enthusiasts, this article details the inner workings of combat damage in Wizards Unite. Combat damage in Wizards Unite follows a relatively simple formula with the following overarching rules:

• Power is used as the base stat from which all damage is calculated.
• Damage from both your combat spells and enemy attacks is consistent and is NOT randomized.
• Enemies are incapable of landing critical hits. However, through random chance, enemies may gain consecutive attacks as mentioned below (as can the player).
• The random factors in combat are three-fold:
• 1) Whether the enemy dodges
• 2) Whether your spell lands a Critical Hit
• 3) Whether you or the enemy gain a consecutive attack phase (how this is determined is still under research)

This damage formula is empirically derived from a combination of self-collected screenshots and data available from the data wrapper. The formula was derived independently from PAndras96's formula, but was cross-validated with his results and are in agreement, with a few qualifications, such as the ceiling (rather than round) function being used for final integer damage values.

## Enemy Stats Information

Below is an image depicting an enemy encounter in a fortress, which provides information about the encounter.

• Proficiency / Deficiency is indicated with a green or red arrow respectively, next to the enemy's affinity.
• Level determines an enemy's effective stats when conducting battle with them. Power, Stamina, Proficiency Power, and Deficiency Defense generally scale with level. For most enemies, the other parameters (Defence, Dodge) do not change with level.
• Difficulty determines the enemy's base stats. Difficulty tiers also follow a generally consistent naming convention:
• ★: Common
• ★★: Formidable
• ★★★: Imposing
• ★★★★: Dangerous
• ★★★★★: Fierce
Enemy Stat Formula

The formula for calculating enemy stats is as follows:

$$Enemy Stats = Base Stat + (Base Stat * Lvl * GrowthAdj)$$

• GrowthAdj: "GrowthAdjustment" - A value that determines how the corresponding stat varies by the enemy's level. The value is currently hidden within in the Data Wrapper, but a tool is in development to allow players to calculate expected enemy stat information.

## The Damage Formula

Below are all formulas relevant to damage and combat. This is also when things get dense and cryptic. The bolded formulae are simplified to help readers understand the overall role of each part of the damage formula.

$$Crit Chance = Precision$$

Critical chance is simply equal to the player's Precision stat.

$$Enemy Dodge Chance = Enemy\texttt{_}Dodge - Accuracy$$

The chance of an enemy dodging is simply the player's Accuracy stat subtracted from the enemy's Dodge stat. This value cannot go below 0.

### Damage

$$Dmg = PowMod * ProfMod * Enemy DefMod * CritMod$$

This is the simplified damage formula. Damage is a combination of Power (PowMod), Proficiency Power (ProfMod), Defence (Enemy DefMod), and Critical damage modifier (CritMod) terms. These are defined in more detail below.

$$\scriptsize{Dmg = Ceiling\texttt{\{}(Power) * }$$

$$\scriptsize{(1 + (IsProficient * Max[0,(ProficiencyPower - Enemy\texttt{_}DeficiencyDefence)])) * }$$

$$\scriptsize{(1-Range[0-100\texttt{%},(Enemy\texttt{_}Defence - DefenceBreach)]) * }$$

$$\scriptsize{(1 + (IsCritical * CriticalPower))\texttt{\}} }$$

The full formula for player damage is shown above.

### Enemy Damage

$$\small{Enemy Dmg = Enemy PowMod * ProfMod * DefMod * ProtegoMod }$$

This is a simplified enemy damage formula. Damage taken from enemies is a combination of their Power (Enemy PowMod), Proficiency Power (ProfMod), your Defence (DefMod), and your Protego Power (ProtegoMod). Each modifier is defined in more detail below.

$$\scriptsize{ Enemy Dmg = Ceiling\texttt{\{}Enemy\texttt{_}Power * }$$

$$\scriptsize{(1 + (Enemy\texttt{_}IsProficient * Max[0,(Enemy\texttt{_}ProficiencyPow - DeficiencyDef)])) * }$$

$$\scriptsize{(1 - Range[0-100\texttt{%},(Defence - Enemy\texttt{_}DefenceBreach)]) * }$$

$$\scriptsize{(1 - (IsProtego * ProtegoPower))\texttt{\}} }$$

The full formula for enemy damage is shown above.

Full List of Combat-Relevant Variables

* Note these terms should include all active buffs and passive skills or conditional effects from professions or potions.

• Power: Base damage dealt by combat spell. Integer.
• ProficiencyPower: % Damage Boost when proficient versus the active enemy. Decimal Format (50% = 0.50).
• DeficiencyDefence: % Damage Reduction from attacks when deficient versus the active enemy. Decimal Format.
• Defence: % Damage Reduction from attacks against any enemy. Decimal Format.
• DefenceBreach: Subtracted from the Enemy's Defence stat. Decimal Format.
• CriticalPower: % Damage Boost when landing a critical hit. Decimal Format.
• ProtegoPower: % Damage Reduction when casting Protego successfully. Decimal Format.
• Precision: % Critical Chance.
• Accuracy: % Reduction of the Enemy Dodge percentage. Cannot go under 0.
• Enemy_Power: The enemy's Power. All enemies have a base power that is adjusted based on their level.
• Enemy_ProficiencyPower: The enemy's Proficiency Power, adjusted based on level.
• Enemy_DeficiencyDefence: The enemy's Deficiency Defence, adjusted based on level.
• Enemy_Defence: The enemy's Defence, adjusted based on level.
• Enemy_DefenceBreach: The enemy's Defence Breach, adjusted based on level.
• Enemy_Dodge: The % chance the enemy will dodge, adjusted based on level.
• IsProficient: This is equal to 1 if you are proficient against the enemy. This is otherwise 0.
• IsCritical: This is equal to 1 if the Critical Hit roll succeeds, and otherwise set to 0.
• IsProtego: This is equal to 1 if the player successfully casts Protego, and otherwise set to 0.
• Enemy_IsProficient: This is equal to 1 if you have a deficiency against the enemy, and otherwise set to 0.
• Max[0,###]: In the formula, this means the value ### cannot go below 0.
• Range[0-100%,###]: In the formula, this means the value ### is capped at either end at 0% or 100%. If exceeding 100%, this is set to 100%, if under 0%, this is set to 0%.

## Potions Affecting Damage

The below is a table displaying the current potions that have a combat-enhancing effect.

 Potion Power Bonus Exstimulo Potion +50% Strong Exstimulo Potion +125% Potent Exstimulo Potion +225% Wit Sharpening Potion +50%(Elite encounters only)
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